Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

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9780199202492: Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.

The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group.

The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford.

This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

About the Author:

Qing Liu is Charge de recherche, Centre National de la Recherche Scientifique (CNRS) Laboratoire de Theorie des Nombres et d'Algorithmique Arithmetique, Universite Bordeaux 1.

Review:


"Although other books do offer a fast passage to modern number theory, ... only Liu provides a systematic development of algebraic geometry aimed at arithmetic."--Choice


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Descrizione libro OUP Oxford, 2006. Paperback. Condizione libro: New. BRAND NEW ** SUPER FAST SHIPPING FROM UK WAREHOUSE ** 30 DAY MONEY BACK GUARANTEE. Codice libro della libreria mon0000814497

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Descrizione libro Oxford University Press, United Kingdom, 2006. Paperback. Condizione libro: New. Language: English . Brand New Book. This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski s Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck s duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo s criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail.The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students. Codice libro della libreria AAZ9780199202492

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Qing Liu (author), Reinie Erne (translator)
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Descrizione libro OUP Oxford 2006-06-29, Oxford, 2006. paperback. Condizione libro: New. Codice libro della libreria 9780199202492

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Descrizione libro Oxford University Press, United Kingdom, 2006. Paperback. Condizione libro: New. Language: English . Brand New Book. This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski s Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck s duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo s criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students. Codice libro della libreria AAZ9780199202492

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Descrizione libro OUP Oxford, 2006. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria FU-9780199202492

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Descrizione libro Oxford University Press. Paperback. Condizione libro: new. BRAND NEW, Algebraic Geometry and Arithmetic Curves, Qing Liu, Reinie Erne, This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students. Codice libro della libreria B9780199202492

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Descrizione libro Oxford University Press, 2006. Condizione libro: New. 2006. Paperback. This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text. Translator(s): Erne, Reinie. Series: Oxford Graduate Texts in Mathematics. Num Pages: 600 pages, illustrations. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational. Dimension: 234 x 158 x 32. Weight in Grams: 872. . . . . . . Codice libro della libreria V9780199202492

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Liu, Qing
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Descrizione libro Oxford University Press. Condizione libro: New. 2006. Paperback. This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text. Translator(s): Erne, Reinie. Series: Oxford Graduate Texts in Mathematics. Num Pages: 600 pages, illustrations. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational. Dimension: 234 x 158 x 32. Weight in Grams: 872. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780199202492

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